I had this same problem. Netflix does an authorization charge on your account to make sure your card is real which depending upon your CC company, it is only a pending charge or refunded later. https://help.netflix.com/en/node/27
This is usually done within a few business days and thus one should not worry about it until maybe a week or two later. Apparently it can take up to 30 days for a refund as well. In my case I never received a refund. After about 5 weeks in total, I checked my account billing info and no refund had been issued. I contacted Netflix through their online chat and it was resolved in less than 5 minutes (I was logged into my account when I did it too).
More or less, if something went wrong and you waited over 30 days, contact them via online chat or phone and hopefully it ll be taken care of just as quickly. I just did it a few minutes ago, so if something goes wrong, I will come back and update this post. If not, assume all went well.